Venn Diagram Worksheet

Venn diagram at a glance

A Venn diagram uses overlapping circles to show the relationship between two or three sets of objects. 

The symbol ξ denotes the universal set. The universal set will usually contain a two or three circle Venn diagram. The intersection of sets within a Venn diagram is where sets overlap; A∩B contains every object that is in A and B. The union of sets describes the objects within multiple regions on a Venn diagram; A∪B contains every object that is in A or B. The complement to a set is every object that is not within the set; A’ is every object not in A. Students study set notation to describe shaded regions on a Venn diagram.

E.g. Let ξ={1,2,3,4,5}, A={Even numbers}, and B={Prime numbers}. Then:

• A∩B={2}, the only even prime number;
• A∪B={2,3,4,5}, even numbers or prime numbers;
• A’={1,3,5}, not an even number (odd numbers).

Venn diagrams are useful as they clearly show the relationship between two sets of data and they can be used to help us work out probabilities. 

Another diagram for organising sets of data is a Carroll diagram. 

Looking forward, students can then progress to additional probability worksheets, for example a probability tree diagram worksheet or how to calculate probability worksheet.

For more teaching and learning support on probability our GCSE maths lessons provide step by step support for all GCSE maths concepts.